Abstract
Machine learning architectures provide a novel perspective on the study of quantum many body states. Restricted Boltzmann machines (RBM) tool is used to represent quantum many-body states in order to find connections to tensor network tools for studying quantum many-body physics, for a deeper understanding of the origin of entanglement entropy in quantum systems. Here, we seek the conditions for the optimal mapping of RBMs into Matrix Product States (MPS), with the aim to show that machine learning methods are a powerful tool for quantum state representations. We here showcase an efficient algorithm for translating RBMs into MPS, with a particular proof for Ising model. We also study the upper entropy bound condition and the entanglement properties of such mapping.
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Howard, E., Chowdhury, I.S., Nagle, I. (2021). Matrix Product State Representations for Machine Learning. In: Silhavy, R. (eds) Artificial Intelligence in Intelligent Systems. CSOC 2021. Lecture Notes in Networks and Systems, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-77445-5_43
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DOI: https://doi.org/10.1007/978-3-030-77445-5_43
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